Pipes and Cistern formulas and Solved Exercise Problems
Best Pipes and Cistern - Aptitude Questions and Answers
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Pipes and Cistern Important Formulas - Aptitude Questions
1.Inlet :
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.
Outlet :
A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.
2. If a pipe can fill a tank in x hours, then :
part filled in 1 hour = 1 / x.
3. I. If a pipe can empty a tank in y hours, then :
part emptied in 1 hour = 1 / y.
II. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes,
then the net part filled in 1 hour = (1 / x - 1 / y).
III. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes,
then the net part emptied in 1 hour = (1 / y - 1 / x).
Pipes and Cisterns Solved Problems
1. Two pipes can fill a tank in 10 hours and 12 hours respectively while a third, pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled?
A. 4 hrs 30 min
B. 7 hrs 30 min
C. 8 hrs 10 min
D. None of these
Answer: B
Explanation:
Net part filled in 1 hour = (1/10) + (1/12)-(1/20) = (8/60) = (2/15).
The tank will be full in 15/2 hrs = 7 hrs 30 min.
2. An electric pump can fill a tank in 3 hours. Because of a leak in, the tank it took 3(1/2) hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
A. 14 hours
B. 16 hours
C. 18 hours
D. 21 hours
Answer: D
Explanation:
Work done by the leak in 1 hour= (1/3)-(1/ (7/2))
= (1/3)-(2/7) = (1/21).
The leak will empty .the tank in 21 hours.
3. Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. After 7 min, C is also opened. In how much time, the tank is full?
A. 17 min
B. 24 min
C. 28 min
D. 39 min
Answer: D
Explanation:
Part filled in 7 min. = 7*((1/36) + (1/45)) = (7/20).
Remaining part= (1-(7/20)) = (13/20).
Net part filled in 1 min. when A, B and C are
opened= (1/36) + (1/45)-(1/30) = (1/60).
Now, (1/60) part is filled in one minute.
(13/20) part is filled in (60*(13/20)) =39 minutes.
4. Two pipes A, B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?
A. 5 min
B. 14 min
C. 8 min
D. 19 min
Answer: C
Explanation:
Let B be closed after x min. then,
Part filled by (A+B) in x min. +part filled by A in (18-x) min = 1
Therefore x*((1/24) + (1/32)) + (18-x)*(1/24) =1
=> (7x/96) + ((18-x)/24) =1.
=> 7x +4*(18-x) =96.
Hence, be must be closed after 8 min.
5. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A. 12 min
B. 15 min
C. 25 min
D. 50 min
Answer: A
Explanation:
Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A + B) in 1 min = (1/20 + 1/30) = 1/12
Both pipes can fill the tank in 12 minutes.
Pipes and Cisterns Exercise Problems and Answers
1. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open,in how many hours will the tank be filled ?
A. 2
B. 2.5
C. 3
D. 3.5
Explanation:
part filled by (A+B+C) in 1 hour = (1/5 + 1/6 + 1/30)
‹=› 1/3.
All the three pipes together will fill the tank in 3 hours.
2. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes ?
A. 5/11
B. 6/11
C. 7/11
D. 8/11
Solution:
Part filled by (A + B + C) in 3 minutes = 3(1/30+1/20+1/10)
= (3×11/60)
= 11/20.
Part filled by C in 3 minutes = 3/10.
Required ratio = (3/10×20/11)
= 6/11.
3. Two taps A and B can fill a tank in 5 hours and 20 hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank ?
A. 8 hrs
B. 9 hrs
C. 18 hrs
D. 36 hrs
Solution:
Part filled by (A + B) in 1 hour = (1/5 + 1/20)
= 1/4.
So, A and B together can fill the tank in 4 hours.
Work done by the leak in 1 hour = (1/4 - 2/9)
= 1 / 36.
Therefore, Leak will empty the tank in 36 hrs.
4. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
A. 8
B. 15
C. 16
D. 18
Answer: D
Explanation:
Capacity of the tank = (12 * 13.5) litres = 162 litres.
Capacity of each bucket = 9 litres
Number of buckets needed = (162/9) = 18.
5. One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. How long will they take to fill the cistern if both the taps are opened ?
A. 5 hrs
B. 7 hrs
C. 6 hrs
D. 8 hrs
Answer: C
Explanation:
Net part filled in 1 hour = (1/2) - (1/3) = 1/6
Cistern will be full in 6 hours.
6. A tap can fill a tank in 16 minutes and another can empty it in8 minutes. If the tank is already half full and both the tanks are oped together, the tank will be:
A. filled in 12 min
B. filled in 8 min
C. emptied in 12 min
D. emptied in 8 min
Answer: D
Explanation:
Rate of waste pipe being more, the tank will be emptied when both the pipes are opened.
Net emptying work done by both in 1 min = (1/8) - (1/16) = 1/16
Now, full tank will be emptied by them in 16 min.
Half full tank will be emptied in 8 min.
7. Two pipes A and B can fill a cistern in 12 minutes and 16 minutes respectively. If both the pipes are opened together, then after how much time B should be closed so that the tank is full in 9 minutes ?
A. 3 min and 30 sec.
B. 4 min and 30 sec.
C. 4 min.
D. 4 min 77 sec.
Answer: C
Explanation:
A tank can be filled by a tap in 20 minutes and by another tap in 6O minutesLet B be closed after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (9 — x) min, = 1
x[(1/12) + (1/16)] + (9 - x)(1/12) = 1 or (7x/48) + (9-x)/12 = 1
or7x + 36 — 4x = 48 or x=4.
So, B must be closed after 4 minutes.
8. A tank can be filled by a tap in 20 minutes and by another tap in 6O minutes. Both the taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in:
A. 10 min
B. 15 min
C. 12 min
D. 20 min
Answer: D
Explanation:
Part filled in 10 min = 10[(1/20) + (1/60)] = 10 * (4/60) = 2/3
Remaining part = (1 - (2/3)) = 1/3
Part filled by second tap in 1 min = 1/60
(1/60) : (1/3) ? 1 : x
Hence, the remaining part will be filled in 20 min.
9. A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
A. 5260
B. 5846
C. 5760
D. 6970
Answer: C
Explanation:
Work done by the inlet in 1 hour = (1/6) - (1/8) = 1/24
Work done by the inlet in 1 min = (1/24) * (1/60) = 1/1440
Volume of 1/1440 part = 4 liters.
Volume of whole = (1440 * 4) litres = 5760 litres.
10. Two taps A and B can fill a tank in 10 hours and 15 hours respectively. If both the taps are opened together, the tank will be full in:
A. 5 hrs
B. 12 and 1/2 hrs
C. 6 hrs
D. 7 and 1/2 hrs
Answer: C
Explanation:
A's hours work=1/10, B's 1 hours work = 1/15,
(A+B)s 1 hours work = (1/10) + (1/15) = 5/30 = 1/6
Both the taps can fill the tank in 6 hours.
11. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. The leak can drain out all the water of the tank in :
A. 10 hours 30 min
B. 21 hours
C. 12 hours
D. 24 hours
Answer: B
Explanation:
Work done by the leak in 1 hour = (1/3) - (2/7) = 1/21 .
Leak will mpty the tank in 21 hours.
12. To fill a cistern, pipes A, B and C take 20 minutes, 15 minutes and 12 minutes respectively. The time in minutes that the three pipes together will take to fill the cistern, is :
A. 5
B. 12
C. 10
D. 15 and 2/3
Answer: A
Explanation:
Part filled by (A +B+ c) in 1 min. = (1/20) +(1/15) + (1/12) = 12/60 = 1/5
All the three pipes together will fill the tank in 5 min.
13. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
A. 4.5 hrs
B. 6.5 hrs
C. 5 hrs
D. 7.2 hrs
Answer : D
Explanation :
Net part filled in 1 hour = (1/4 - 1/9) = 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.